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isosceles wanted, tangent and secant from exterior point of a circle

Source: Switzerland - Swiss MO 2004 p1

July 19, 2020
geometryisoscelestangentsecant

Problem Statement

Let Γ\Gamma be a circle and PP a point outside of Γ\Gamma . A tangent from PP to the circle intersects it in AA. Another line through PP intersects Γ\Gamma at the points BB and CC. The bisector of ∠APB\angle APB intersects ABAB at DD and ACAC at EE. Prove that the triangle ADEADE is isosceles.
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